An application of deterministicaperiodic structures :
Sensing with Plasmonic quasi-crystals Ata Akatay
July 24, 2009
Photonic Crystals - Romuald Houdré
Application ideaperiodic media=> the formation of well-defined energy gapsdisordered random media=> the presence of localized eigenstates with highfield enhancement and Q-factorsdeterministic aperiodic structures=> Suggest solutions in between
« defined by the iterations of simple mathematical rules, rooted in symbolic dynamics, prime number theory and L-system inflations »
Dal Negro, L. and N. N. Feng (2007)
deterministic aperiodic structures
Periodic Fibonacci quasi-periodic structures
Thue–Morse and aperiodic structures
Rudin–Shapiro structures
absolutely continuoussingular continuous
quasiperiodic
Dal Negro, L. and N. N. Feng (2007)
Fractal Fourier spectra
Fibonacci quasi-periodic structures
Thue–Morse and aperiodic structures
Rudin–Shapiro structures
Dal Negro, L. and N. N. Feng (2007)
Dal Negro, L. and N. N. Feng (2007)
Aperiodic nanoparticle chain
Dal Negro, L., N. N. Feng, et al. (2008)
The dipole equations of motion :
Transfer matrix approach valid within the dipole approximation
Simplifies to : where,
In frequency domain :
and gives :
Dal Negro, L. and N. N. Feng (2007)
Analysis
the integrated density of states (IDS) of the chain:
participation ratio yields a quantitative measure of the localization degree of the eigenstates:
Dal Negro, L. and N. N. Feng (2007)
Dal Negro, L. and N. N. Feng (2007)
Dal Negro, L., N. N. Feng, et al. (2008)
Dal Negro, L., N. N. Feng, et al. (2008)
Conclusion
whispering-gallery (WG) mode microcavitieslow shifts of modal frequenciesSP sensors, which benefit from high values of field intensities in the detection regionbroad resonance linewidths (low Q-factors), which is a limiting factor in the spectral resolution of such devices.
deterministic aperiodic structuresCan be designed for more flexible solutions
References1. Dal Negro, L. and N. N. Feng (2007). "Spectral gaps
and mode localization in Fibonacci chains of metal nanoparticles." Optics Express 15(22): 14396-14403.
2. Dal Negro, L., N. N. Feng, et al. (2008). "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays." Journal of Optics a-Pure and Applied Optics 10(6): -.